Spaces of type BLO for non-doubling measures
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- by Yinsheng Jiang PDF
- Proc. Amer. Math. Soc. 133 (2005), 2101-2107 Request permission
Abstract:
The spaces of type BLO for the positive Radon measures satisfying a growth condition on $\mathbb R^d$ are introduced. It is shown that some properties which hold for the classical space BLO when $\mu$ is a doubling measure remain valid for the spaces of type BLO introduced in this paper, without assuming $\mu$ doubling.References
- Colin Bennett, Another characterization of BLO, Proc. Amer. Math. Soc. 85 (1982), no. 4, 552–556. MR 660603, DOI 10.1090/S0002-9939-1982-0660603-5
- R. R. Coifman and R. Rochberg, Another characterization of BMO, Proc. Amer. Math. Soc. 79 (1980), no. 2, 249–254. MR 565349, DOI 10.1090/S0002-9939-1980-0565349-8
- M. A. Leckband, Structure results on the maximal Hilbert transform and two-weight norm inequalities, Indiana Univ. Math. J. 34 (1985), no. 2, 259–275. MR 783915, DOI 10.1512/iumj.1985.34.34016
- F. Nazarov, S. Treil, and A. Volberg, Weak type estimates and Cotlar inequalities for Calderón-Zygmund operators on nonhomogeneous spaces, Internat. Math. Res. Notices 9 (1998), 463–487. MR 1626935, DOI 10.1155/S1073792898000312
- E. M. Stein, Singular integrals, harmonic functions, and differentiability properties of functions of several variables, Singular Integrals (Proc. Sympos. Pure Math., Chicago, Ill., 1966) Amer. Math. Soc., Providence, R.I., 1967, pp. 316–335. MR 0482394
- Xavier Tolsa, BMO, $H^1$, and Calderón-Zygmund operators for non doubling measures, Math. Ann. 319 (2001), no. 1, 89–149. MR 1812821, DOI 10.1007/PL00004432
Additional Information
- Yinsheng Jiang
- Affiliation: Department of Mathematics, Xinjiang University, Urumqi, 830046, People’s Republic of China
- Email: ysjiang@xju.edu.cn
- Received by editor(s): November 22, 2003
- Received by editor(s) in revised form: March 24, 2004
- Published electronically: January 31, 2005
- Additional Notes: The author was supported in part by NSFC Grant #10261007.
- Communicated by: Andreas Seeger
- © Copyright 2005
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Proc. Amer. Math. Soc. 133 (2005), 2101-2107
- MSC (2000): Primary 42B20, 42B25, 42B35
- DOI: https://doi.org/10.1090/S0002-9939-05-07795-6
- MathSciNet review: 2137877